General background of nuclear magnetic resonance (NMR) well logging is set forth in copending U.S. patent application Ser. No. 08/873,582, assigned to the assignee hereof, and in U.S. Pat. No. 5,023,551. Briefly, in NMR operation the spins of nuclei align themselves along an externally applied static magnetic field. This equilibrium situation can be disturbed by a pulse of an oscillating magnetic field (e.g. an RF pulse), which tips the spins away from the static field direction. After tipping, two things occur simultaneously. First, the spins precess around the static field at the Larmor frequency, given by .omega..sub.0 =.gamma.B.sub.0, where B.sub.0 is the strength of the static field and .gamma. is the gyromagnetic ratio. Second, the spins return to the equilibrium direction according to a decay time T1, the spin lattice relaxation time. For hydrogen nuclei, .gamma./2.pi.=4258 Hz/Gauss, so, for example, for a static field of 235 Gauss, the frequency of precession would be 1 MHz. Also associated with the spin of molecular nuclei is a second relaxation, T2, called the spin-spin relaxation time. At the end of a ninety degree tipping pulse, all the spins are pointed in a common direction perpendicular to the static field, and they all precess at the Larmor frequency. However, because of small inhomogeneities in the static field due to imperfect instrumentation or microscopic material heterogeneities, each nuclear spin precesses at a slightly different rate. T2 is a time constant of this "dephasing".
A widely used technique for acquiring NMR data both in the laboratory and in well logging, uses an RF pulse sequence known as the CPMG (Carr-Purcell-Meiboom-Gill) sequence. As is well known, after a wait time that precedes each pulse sequence, a ninety degree pulse causes the spins to start precessing. Then a one hundred eighty degree pulse is applied to keep the spins in the measurement plane, to cause the spins which are dephasing in the transverse plane to reverse direction and to refocus. By repeatedly reversing the spins using one hundred eighty degree pulses, a series of "spin echoes" appear, and the train of echoes is measured and processed.
Identification of the presence of gas in a formation is one of the most important tasks of petrophysical log interpretation. Since NMR is a proton measurement, it is somewhat analogous to the porosity measurement with a neutron tool; namely, it is sensitive to the hydrogen index of the formation, which is significantly reduced in gas. However, unlike the neutron tool, the NMR measurement is insensitive to neutron absorbers, crystalline waters of hydration, and lithology. A so-called "Amplitude Method" takes advantage of this to evaluate the gas volume of the formation. The Amplitude Method is summarized, for example, in Flaum, C., Kleinberg, R., and Hurlimann, M., Identification Of Gas With The Combinable Magnetic Resonance Tool (CMR), Paper L. SPWLA, 37th Annual Logging Symposium, New Orleans, Jun. 16-19, 1996.
Recently, much attention has been focused on a secondary phenomenon which can be exploited to use NMR for an independent indication of gas; namely, diffusion. Exploitation of the diffusion process is based on the fact that molecular diffusion is more rapid in gas than in water or most liquid hydrocarbons.
Diffusion can have a significant effect on the pulsed NMR measurement, since a diffusing molecule with a polarized proton can be displaced an appreciable distance between successive pulses. If the static magnetic field is not uniform, this displacement will cause a dephasing of the transverse magnetization. The result is a noticeable decrease in the relaxation time T.sub.2, or a shift in the T.sub.2 distribution spectrum to shorter times.
Among the techniques that have been suggested for obtaining gas-related measurements are techniques known as Differential Spectrum, Shifted Spectrum, Matched Filter, and Echo Ratio methods.
The Differential Spectrum Method (DSM) involves acquiring a difference between T.sub.2 distributions at two different polarization times, taking advantage of long T.sub.1 relaxation time of the gas. [Reference can be made to R. Akkurt et al., NMR Logging of Natural Gas Reservoirs, Paper N, SPWLA 36th Annual Logging Symposium, 1995.] The observed difference reflects the change in the amount of polarization of the gas phase, while signal from the water phase is canceled out. The oil phase, if it is present, may contribute to and distort the result.
The Shifted Spectrum Method (SSM) takes advantage of the large diffusion coefficient of the gas phase. [Reference can again be made to Akkurt et al., supra.] It involves acquiring a difference between T.sub.2 distributions at two different echo spacings, since diffusion effect is sensitive to echo spacing. Signal from non-diffusing components cancels out in the difference, and the remainder is an "S" shaped distribution from the gas phase. A limitation of this technique is that the details of the shape of T.sub.2 distributions may be affected by factors other than gas presence.
The Echo Ratio Method (ERM) is an improvement over SSM, in that the difference is obtained in the time domain, avoiding certain distortions that occur when transforming from time domain to T.sub.2 domain. [Reference can be made, for example, to C. Flaum et al., Identification Of Gas With Combinable Magnetic Resonance Tool ("CMR"), 1996, supra, and to the above-referenced copending U.S. patent application Ser. No. 08/873,582. ] A limitation of this technique is that the residual signal is small, and it is necessary to compare signals at different echo spacings.
The Matched Filter Method (MFM) is a combination of DSM and SSM, but the difference is obtained in the time domain, and the result is fitted to one or two "basis functions" (filters) to obtain volumes of gas or oil and gas. [Reference can be made to M. G. Prammer et al., Lithology-Independent Gas Detection By Gradient-NMR Logging, Society Of Petroleum Engineers, SPE 30562, 1995.] The water signal cancels out. The general method involves two sets of data with different wait times and different echo spacings. The method does rely on a priori knowledge of the properties (bulk T2 relaxation times and diffusion coefficients of the oil and gas phases).
An application of MFM involves two data sets with largely contrasting wait times (T.sub.W) but the same (relatively long, e.g. 1 ms) echo spacings (T.sub.E). In this method, the water signal cancels out, and the gas and oil signals are widely separated in T.sub.2 space due to large contrast in diffusion in the two phases. A mere presence of signal at low T.sub.2 is already a gas indication. A matched filter fit to the echo difference yields a quantitative answer. The matched filters, or response functions, for this case would be: EQU f(t).sub.oil =[e.sup.-T.sbsp.W1.sup./T.sbsp.1-oil -e.sup.-T.sbsp.W2.sup./T.sbsp.1-oil ]e.sup.-t/T*.sbsp.2-oil(1a) EQU f(t).sub.gas =HI.sub.gas [e.sup.-T.sbsp.W1.sup./T.sbsp.1-gas -e.sup.-T.sbsp.W2.sup./T.sbsp.1-gas ]e.sup.-t/T*.sbsp.2-gas(1b)
where T.sub.W1 and T.sub.W2 are the respective wait times, T.sub.1-oil and T.sub.1-gas are the spin lattice relaxation times of bulk oil and gas, respectively, HI.sub.gas is the hydrogen index of the gas, and the asterisk on T.sub.2 's indicates that it is affected by diffusion, as given by the equation: EQU 1/T*.sub.2 =1/T.sub.2-bulk +1/T.sub.2-D (2)
T.sub.2-D is a known function of diffusion coefficient and echo spacing.
It has been generally understood that the foregoing MFM technique requires use of an NMR logging tool having a constant gradient of static magnetic field. A constant gradient implies a constant diffusion effect. In T.sub.2 space, the gas signal will be shifted by diffusion, but still appear as a narrow peak in a constant gradient. In NMR logging devices with a broad magnetic field gradient distribution [see, for example, the type of logging device disclosed in U.S. Pat. No. 5,055,788], the gas signal in T.sub.2 space will be significantly broadened by diffusion, presumably making it difficult, if not impossible, to identify, especially in the presence of normal noise.
It is among the objects of the present invention to overcome limitations of prior art NMR techniques for detecting and characterizing hydrocarbons in earth formations.